Some of the Toto toilets allow the bowl to move forward or backward 2"
They would be the ones that have the Unifit adapter.
They come standard for a 12" rough, and 10"'s and 14"'s can be ordered.
Since you are going for 4", not 2", then the decision is whether the plumbers should move the drain itself.
With four inches, it looks like the plumber will be going into the crawlspace, and depending on what he sees, and his ability, he can make the 4" change. He might do it in Cast, or he may convert to plastic.
Either way, with the open space you mention, it should be doable.
If the plumber is in the crawlspace, he might as well move it, and not do an "offset" flange.